Ok, so I started by adding a Levels layer, and on the Red channel, moving the middle slider to 1.50.
Then inverted the mask, then gently painted over the rainbow, along the red area, slowly building up a bit of red glow.
My mask looked like this:
Then I duplicated that Levels layer, and on that new layer, I put the Red channel back to normal, and instead moved the middle slider on the Green channel to 1.50.
Then I chose the Move Tool, and nudged the layer across to the right a bit, to create the green part of the rainbow.
Then I repeated that process one more time - duplicated the layer, put the Green back to normal, and put the Blue middle slider on 1.50, then nudged it across some more.
Here's what the layers panel looked like at the end: